Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+4y &= -4 \\ -8x+8y &= 1\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = -8y+1$ Divide both sides by $-8$ to isolate $x$ $x = {y - \dfrac{1}{8}}$ Substitute this expression for $x$ in the first equation. $-5({y - \dfrac{1}{8}}) + 4y = -4$ $-5y + \dfrac{5}{8} + 4y = -4$ Simplify by combining terms, then solve for $y$ $-1y + \dfrac{5}{8} = -4$ $-1y = -\dfrac{37}{8}$ $y = \dfrac{37}{8}$ Substitute $\dfrac{37}{8}$ for $y$ in the top equation. $-5x+4( \dfrac{37}{8}) = -4$ $-5x+\dfrac{37}{2} = -4$ $-5x = -\dfrac{45}{2}$ $x = \dfrac{9}{2}$ The solution is $\enspace x = \dfrac{9}{2}, \enspace y = \dfrac{37}{8}$.